A078052 Expansion of (1-x)/(1+x+2*x^2+2*x^3).

1, -2, 0, 2, 2, -6, -2, 10, 6, -22, -10, 42, 22, -86, -42, 170, 86, -342, -170, 682, 342, -1366, -682, 2730, 1366, -5462, -2730, 10922, 5462, -21846, -10922, 43690, 21846, -87382, -43690, 174762, 87382, -349526, -174762, 699050, 349526, -1398102, -699050, 2796202, 1398102, -5592406, -2796202

Offset

0,2

Comments

First differences of A077980.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,-2,-2)

Formula

a(n) = (1/3) * ((-3+5*(-1)^n)/2 * (-2)^floor(n/2) + 2*(-1)^n ). - Ralf Stephan, Aug 17 2013

a(0)=1, a(1)=-2, a(2)=0, a(n)=-a(n-1)-2*a(n-2)-2*a(n-3). - Harvey P. Dale, Mar 26 2015

Mathematica

CoefficientList[Series[(1 - x) / (1 + x + 2 x^2 + 2 x^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{-1, -2, -2}, {1, -2, 0}, 50] (* Harvey P. Dale, Mar 26 2015 *)

Prog

(PARI) a(n)=1/3*((-3+5*(-1)^n)/2*(-2)^floor(n/2)+2*(-1)^n); \\ Ralf Stephan, Aug 17 2013
(Magma) I:=[1, -2, 0]; [n le 3 select I[n] else -Self(n-1)-2*Self(n-2) -2*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 17 2013

Crossrefs

Sequence in context: A071055 A183034 A354101 * A056458 A322509 A284570

Adjacent sequences: A078049 A078050 A078051 * A078053 A078054 A078055

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved